A210425 Number of 3-divided words of length n over a 4-letter alphabet.

0, 0, 4, 60, 374, 1960, 9103, 40497, 174127, 735268, 3064477, 12664101, 52005445, 212595280, 866047122

Offset

1,3

Comments

See A210109 for further information.

Row sums of the following table which shows how many words of length n over a 4-letter alphabet are 3-divided in k>=1 different ways:

4;

41, 14, 5;

147, 111, 67, 29, 14, 6;

594, 358, 381, 211, 156, 128, 80, 28, 17, 7;

2072, 1400, 1433, 875, 821, 669, 588, 369, 340, 240, 163, 72, 33, 20, 8;

- R. J. Mathar, Mar 25 2012

Links

Table of n, a(n) for n=1..15.

Prog

(Python)
from itertools import product
def is3div(b):
    for i in range(1, len(b)-1):
        for j in range(i+1, len(b)):
            X, Y, Z = b[:i], b[i:j], b[j:]
            if all(b < bp for bp in [X+Z+Y, Z+Y+X, Y+X+Z, Y+Z+X, Z+X+Y]):
                return True
    return False
def a(n): return sum(is3div("".join(b)) for b in product("0123", repeat=n))
print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Aug 30 2021

Crossrefs

Cf. A210109, A210426.

Sequence in context: A060492 A234952 A112041 * A366690 A002060 A247739

Adjacent sequences: A210422 A210423 A210424 * A210426 A210427 A210428

Keyword

nonn

Author

R. J. Mathar, Mar 21 2012

Extensions

a(12)-a(15) from Michael S. Branicky, Aug 30 2021

Status

approved